We recently came across a quote by the English writer and philosopher G.K. Chesterton: “It isn’t that they can’t see the solution. It’s that they can’t see the problem.” Problem solving in math class requires more than procedural skills. Students must first understand the problem before attempting a solution and explaining their thinking. This can present a challenge in our classrooms.
Bar modeling can be a tool to help teachers and students meet this problem-solving challenge. It is often considered the hallmark of Singapore Math® and can help students “see” the problem by representing known and unknown quantities and their relationships (sounds sneakily algebraic, doesn’t it?).
Let’s consider the following problem:
On Halloween, Logan ended up with seven fewer pieces of candy then Kristin. They have 55 pieces of candy altogether. Find the number of pieces Logan has.
Students who don’t understand the problem may mistakenly subtract based upon the word “fewer.” For those of us who remember algebra, we can represent the problem this way: 2x + 7 = 55. Algebraically, we would isolate the variable and solve for x (x = 24; Logan has 24 pieces of candy). Although perfectly acceptable, the algebraic solution is abstract and developmentally inaccessible to most elementary students, yet they still need to solve this type of problem. Bar modeling can make it more accessible.
Let’s draw a bar for Logan and a bar for Kristin. At this point, I’m not quite sure how long to draw the bars, but I know that Logan’s will be shorter because he has fewer pieces of candy.